Exponential Separation of Quantum and Classical One-Way Numbers-on-Forehead Communication
Guangxu Yang, Jiapeng Zhang

TL;DR
This paper proves the first exponential separation between quantum and classical one-way NOF communication complexity by analyzing a lifted Hidden Matching problem, demonstrating quantum efficiency versus classical limitations.
Contribution
It establishes the first explicit exponential separation in one-way NOF communication complexity between quantum and classical protocols.
Findings
Quantum protocol for the problem has $O(\log n)$ cost.
Classical randomized protocols require $\Omega(n^{1/3}/2^{k/3})$ communication.
Separation applies even with multiple communicating players.
Abstract
Numbers-on-Forehead (NOF) communication model is a central model in communication complexity. As a restricted variant, one-way NOF model is of particular interest. Establishing strong one-way NOF lower bounds would imply circuit lower bounds, resolve well-known problems in additive combinatorics, and yield wide-ranging applications in areas such as cryptography and distributed computing. However, proving strong lower bounds in one-way NOF communication remains highly challenging; many fundamental questions in one-way NOF communication remain wide open. One of the fundamental questions, proposed by Gavinsky and Pudl\'ak (CCC 2008), is to establish an explicit exponential separation between quantum and classical one-way NOF communication. In this paper, we resolve this open problem by establishing the first exponential separation between quantum and randomized communication complexity…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Quantum Computing Algorithms and Architecture · Cryptography and Data Security
